Inferred cosmic-ray spectrum from ${it Fermi}$-LAT $gamma$-ray observations of the Earths limb

Recent accurate measurements of cosmic-ray (CR) species by ATIC-2, CREAM, and PAMELA reveal an unexpected hardening in the proton and He spectra above a few hundred GeV, a gradual softening of the spectra just below a few hundred GeV, and a harder spectrum of He compared to that of protons. These newly-discovered features may offer a clue to the origin of high-energy CRs. We use the ${it Fermi}$ Large Area Telescope observations of the $gamma$-ray emission from the Earths limb for an indirect measurement of the local spectrum of CR protons in the energy range $sim 90~$GeV-$6~$TeV (derived from a photon energy range $15~$GeV-$1~$TeV). Our analysis shows that single power law and broken power law spectra fit the data equally well and yield a proton spectrum with index $2.68 pm 0.04$ and $2.61 pm 0.08$ above $sim 200~$GeV, respectively.